Nonlocality effect in $α$ decay half-lives for even-even nuclei within a two potential approach

TL;DR

This work extends the two-potential approach for alpha decay by incorporating a coordinate-dependent effective mass to account for nonlocality in the alpha-nucleus interaction, and applies it to 196 even-even nuclei. By adjusting a global parameter ρ_S, the model achieves a notable improvement in agreement with experimental half-lives, reducing the log-deviation standard deviation from 0.573 to 0.522. The authors propagate the approach to predict alpha-decay properties for Z = 118 and Z = 120 isotopes using Qα values from WS4, RCHB, and FRDM mass models, and they analyze shell effects, finding robust N = 184 features across models and model-dependent N = 178 behavior. These results enhance predictive capability for superheavy nuclei and provide guidance for future experimental investigations.

Abstract

In this paper, we carefully look at the $α$ -decay half-lives of 196 even-even nuclei using a two-potential approach that is made better by taking into account an alpha particle's effective mass that changes with coordinates. The result shows that the accuracy of this model has been improved after considering effective mass for the alpha particle. Furthermore, considering $α$ decay energies derived from three mass models, namely the Weizsacker-Skyrme-4 (WS4) mass model, the relativistic continuum Hartree-Bogoliubov theory mass model, and the FRDM (2012), we extend this model to predict the $α$ -decay half-lives of Z = 118 and 120 isotopes. Finally, we carefully study the predicted $α$ decay energies and half-lives of Z = 118 and 120 isotopes and discuss the shell structure of superheavy nuclei. We found that the shell effect is obvious at N = 178 and at N = 184 in the WS4 mass model and FRDM(2012), while the shell effect is only obvious at N = 184 in the relativistic continuum Hartree-Bogoliubov theory mass model.

Figures (5)

• Figure 1: The difference in logarithmic form of $\alpha$ decay half-lives between calculated data and experimental. The abscissa is the mass number A and ordiante is the value of $log_{10}(T_{1/2}^{cal}/T_{1/2}^{exp})$. The red dot and black square represent the theoretical value calculated by using the TPA without considering nonlocality effect and after considering nonlocality effect, respectively.
• Figure 2: The contribution of the nonlocal effect on tunneling calculations. Selected example for $\alpha$-decay from $_{78}^{184m} Pt$ : effective reduced mass $\mu$ considering nonlocality effect with $\rho_{s} = 0.595$.
• Figure 3: The contribution of the nonlocal effect on tunneling calculations. Selected example for $\alpha$-decay from $_{78}^{184m} Pt$ : comparison between the functions $f(r)$ in the integrand of the barrier penetrability: considering the reduced masses $\mu$ (blue line $\rho_{S} = 0$ and $\mu_{0}$ (red line $\rho_{S} = 0.595$)).
• Figure 4: $\Delta \tau$-distributions for 196 $\alpha$-emitters. (a) Result for the calculations with $\rho_{s} = 0$ (without nonlocality effect). In this case, most of the calculated half-lives are bigger than the experimental values, which can be observed with the centroid being shifted to the positive values $\Delta \tau$ = 47.232. (b) The centroid is exactly on $\Delta \tau$ = 0 when the nonlocality effect is considered in the calculation with $\rho_{s}$ = 0.595.
• Figure 5: The value of $Q_{\alpha}$ and predicted $\alpha$ decay half-lives for even-even nuclei with Z = 118 and 120 isotopes. The black square and red dot indicate Z = 118 and Z = 120, respectively. The abscissa is neutron number $N$, the ordinate in the left column is $Q_{\alpha}$ in MeV, and the ordinate in the right column is logarithm $log_{10}T_{1/2}$ of calculated half-life in s. The mass tables used from top to bottom in this figure are RCHB, WS4, FRDM.